A recent and promising line of research [1]}, [2]}, [3]}, [4]} aimed to redattain disentanglement do this in a fully unsupervised way, relying on a probabilistic interpretation of disentanglement according to which a representation is defined to be disentangled if the
data distribution can be modeled as a nonlinear transformation of a product of independent probability
distributions. Unfortunately, similarly to the ICA case, this leads to pessimistic results [5]} in terms of the identifiability of the factors without any assumptions on the model or the data (inductive bias).
In this work we propose a different definition of disentanglement, which is entirely based on the geometric notion of metric and manifolds, and we rely on the assumption on observing non i.i.d. samples as data – thus escaping the non-identifiability result of [5]}.
